Sen. Marco Rubio (R) of Florida arrives at the Senate chamber for a vote on Monday. One of the immigration bill’s authors, Senator Rubio has already acknowledged that the bill will face a tough road to passage if the border security elements are not improved.

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Washington — Senate conservatives in a hearing Tuesday took aim at a key border security element of the immigration reform bill, peppering the leaders of federal agencies charged with securing the nation’s borders to try to firm up what, exactly, counts as a secure border.

As a Senate committee begins amending the bill this week, the concern among senators such as Sen. Tom Coburn (R) of Oklahoma will likely become an even greater part of the immigration reform debate – and perhaps the shape of the final legislation – in the weeks to come.

The reform bill’s bipartisan sponsors have vowed to pursue more Republican support for the measure. As they offer amendments, outspoken Republicans like Senator Coburn are outlining exactly what it would take to get them on board.

To pass an immigration reform measure in the GOP-lead House, Coburn pointed out at Tuesday's hearing, “we're going to have to do a whole lot more on what is the definition of a ‘controlled border’ than what is in this bill.”

“If, in fact, we really want this to happen, we have to start addressing this now,” the iconoclastic Sooner and the committee’s top GOP member said. “And you can't have any false observations on this. The political reality is the American people want to know the border's controlled.”

To address such concerns, the bipartisan Senate bill sets a target: The US will, with the help of $4.5 billion in new border security funding, turn back or apprehend 90 percent of potential border-crossers in high-risk areas within five years after passage.

If that level of control isn’t in place within five years, the bill authorizes an additional $2 billion in funding and requires a group of border-state elected officials and community leaders to certify when the border is secure. None of the estimated 11 million undocumented people in the US will be allowed to obtain permanent residency without a certified, secure southern border, the bill says.

But Republicans aren't convinced that the Department of Homeland Security can accurately confirm that 90 percent figure. Several senators asked witnesses at the hearing: How can DHS credibly estimate how many people are trying to cross the border? Moreover, they added, why, exactly, is the bill staking so much on a seemingly arbitrary number?

Asked why 90 percent was the appropriate figure for a safe, secure America, US Border PatrolChief Michael Fisher said, “Basically it's because ... it's an ‘A.’ If you're going to set a goal for border security and national security, anything less than, at a minimum, 90 percent would be untenable in terms of a goal.”

In addition, what vexes those like Republican Sens. Ron Johnson of Wisconsin and Rand Paul of Kentucky is not any particular number but that the legislation doesn’t specify much of anything to get to the 90 percent threshold.

What the bill does require is for the secretary of Homeland Security to lay out two plans: one for general border security and one specifically on border fencing, in order to reach a 90 percent apprehension rate over the next half-decade. If those fail, the committee of border state eminences must make the call.

“I don't know what happens if the commission doesn't do anything,” said Senator Paul, who asked earlier this week that the Homeland Security Committee be allowed to amend the bill, after it passes the Senate Judiciary Committee, where it currently resides.

Paul compared the bill to President Obama’s signature health-care law, in the sense that it has nearly 2,000 references to issues that a cabinet secretary (in this case, usually of the Department of Homeland Security) will have to decide in the future.

Why isn’t Congress making the rules, Paul questioned.

“We don't write bills around here,” he added, with some scorn. “We should write the bill. We should write the plan.”

Mr. Fisher and others said that the bill’s funding and comprehensive approach to the immigration issue would allow authorities to shore up efforts that have, alongside changing economic conditions on both sides of the Rio Grande, produced a net flow of no illegal immigration in recent years.

“I think because of the work-site enforcement, because of the technology deployment, because of the streamlining of immigration laws, if you put all of that together, our ability to have better control of the borders, I think, will also improve,” said David Heyman an assistant secretary for policy at the Department for Homeland Security (DHS). “And so we're confident that it's the right formula.”

Senate GOP sponsors, too, say that the bill's border security provisions could be strengthened – and must be for the bill to pass.

"The federal government’s failure to enforce the law in the past has left people with little confidence in its ability to do so in the future," said Sen. Marco Rubio (R) of Florida, in a statement. "That is why in order for this bill to become law, it will have to be improved to bolster border security and enforcement even further and to limit the federal government’s discretionary power in applying the law."

While Coburn lauded DHS for producing better border security data “than what we've ever had before” he added that conservative support for the bill won’t turn on data – but it may very well hinge on how effective lawmakers think those changes will be.

“The question is whether or not [the changes are] adequate, because if we had 98 percent control and the 2 percent [left uncontrolled] were terrorists, we wouldn't think that was control,” he said.